Two of my cats had upper respiratory infections as kittens, and I would spend a few minutes with them cradled in my arm while I scraped gunk out of their eyes and noses so they could see and breathe better, and giving them their medication.

By the time they were over their colds, they would just lay there quietly, patiently. They seem to like being held that way now.

My eldest cat often has a little discharge in the corner of his eyes. I'm having some limited success doing the same thing, just gently grooming his face with one hand, while scruffing him on his side or back with the other. He prefers wrestling to cuddling, though. He tolerates me touching his face only if I have my hand on the back of his neck. As soon as I let go, it's wrestling time again.